Growth of Single Crystals High temperature methods Czochralski Stockbarger and Bridgman Verneuil Zone melting Medium temperature methods Fluxes Electrochemical from melts Hydrothermal Vapor phase transfer Sublimation Solution Gel Low temperature methods i Growth of Single Crystals Crystallization techniques: vapor, liquid, solid phase Single crystals # vital for meaningful property measurements of materials # allow measurement of anisotropic phenomena (electrical, optical, magnetic, mechanical, thermal) in anisotropic crystals (symmetry lower than cubic) é* fabrication of devices Y3A15012 (YAG = yttrium aluminum garnet) and beta-beryllium borate (BBO) for doubling and tripling the frequency of CW or pulsed laser light Si02 (quartz) crystal oscillators for mass monitors lithium niobáte for photorefractive applications Many different crystal growing techniques exist, hence one must think very carefully as to which method is the most appropriate for the material under consideration, size of crystal desired, stability in air, morphology or crystal habit required 2 Solidification of Materials a material cools off the average kinetic energy drops Energy Ea Crystallization Nucleation - formation of nuclei of critical size Crystal growth - diffusion of material toward the crystal, depositon vs. dissolution 4 Formation of Nuclei Molecules are always bumping into each other - sometimes they stick At lower kinetic energies more molecules stick together = form nuclei Cooling Solidification The energy of the crystal structure is less than that of the liquid The difference = the volume free energy AGV As the solid grows in size, the magnitude of the total volume free energy increases (a negative value) When solids form in a liquid there is an interface created The surface free energy, ySL = the solid/liquid interfacial energy associated with this interface (changed in different solvents) As the solid grows, the total surface free energy increases (a positive value) 6 Solidification The total change in free energy for the system is the sum of the two factors. For spherical nuclei AG = 4/3 ti r 3AGV + 4tt r 2 ySL The volume free energy goes up with the cube of the radius The surface free energy goes up with the square of the radius AG has a maximum at a critical radius - critical free energy AGC If just a few molecules stick together, they will redissolve If enough molecules stick together, the embryo will grow 7 Nucleation Retarding energy AGS = surface free-energy change = 4n-r27 A/^ = total free-energy change Radius of particle, r r: radius of spheric seed r*: critical radius (r>r* seed grows by itself) AGN: total free energy change AGS: surface free energy change AGV: volume free energy change ■ AGV ~ volume free-energy change = I ^ AGV AGN = 47ir2ySL + 4/37ir3AG, 8 Volume Free Energy RTlnS AGV =----------- V m AGy - the free energy change between the 'monomer' in solution and unit volume of bulk crystal S - supersaturation = the quotient of the actual concentration and the concentration of the respective species at equilibrium conditions, indicates how far away from equilibrium the system is. V - molar volume of the bulk crystal Total Free Energy of a Solid-Liquid System AG i Surface Energy 4jl xi Ys^/ 111 ■ 1111 ■ 111 : ^~ww— . . 2e-0B7 . . 3e-08. . . 4e-08 -----------^ž k Critical Radius ^v Volume r 4/3 ti r 3AGV \ 10 Supersaturated Solutions If the liquid is just at the freezing point, only a few molecules stick, because they have comparatively high energy As the liquid is cooled, more molecules can form into nuclei. When the nucleus is big enough (because of undercooling) the supercooled liquid suddenly changes to a solid. 11 Homogeneous Nucleation - Critical Radius rc critical radius is: 2ľu. 2ľn.K ^ __ - SL __ / SL m S = supersaturation / — — AGV RT In S At larger supersaturation, the critical radius of nuclei is smaller 12 Critical Free Energy AG .3 t^3 AG =- 16aysLV* 3(RT In S) The free energy necessary to form stable nuclei 13 Rate of Nucleation AGC - the free energy barrier to nucleation S - supersaturation Vm- molar volume of the bulk crystal Arrhenius dN A f ----= A exp dt \ kT \ J í = ÄQXp 3 T^3 MnrLK \ V 3k3T3N2A(\nS) J 14 Homogeneous Nucleation The process is called homogeneous nucleation It only occurs if the material is very pure The size of the critical radius is: * 2YsLTn r =________- — "> AT is the undercooling Metals often experience undercooling of 50 to 500 °C AHfAT 15 LaMer Plot I U m ■ j c 5=SC ■ / \ ■/ 1 o 4-» 2? S i H—» tu £ a> Q. 3 CO S=1 / -1------------- í ------------• Burst nucleation - many nuclei generated at the same time, then the nuclei grow without additional nucleation, all of the particles nucleate simultaneously, their growth histories are the same. Control of the size distribution of the ensemble of particles during growth -synthesis of monodisperse nanocrystals 16 The concentration of "monomer", (the minimum subunit of bulk crystal) constantly increases with time. Stage I precipitation does not occur even under supersaturated conditions (S>1), the energy barrier for spontaneous homogeneous nucleation is too high. Stage II nucleation occurs, the degree of supersaturation is high enough to overcome the energy barrier for nucleation, the formation and accumulation of stable nuclei. The rate of monomer consumption exceeds the rate of monomer supply, the monomer concentration decreases until it reaches the level at which the nucleation rate is zero. Stage III the growth stage, nucleation stopped, the particles keep growing as long as the solution is supersaturated Growth Growth by diffusion the growth rate of spherical particles (dr/dt) depends only on the flux of the monomers to the particles (J) T 4m*2 dr r a 2r^dC J =------------ J = 47DC2D----- Vm at dx m r+f dx AttD Cf Jr, J ~=~ridc r Cs S 18 Heterogeneous Nucleation Homogeneous nucleation usually only occurs in the lab. Impurities provide a "seed" for nucleation Solidification can start on a wall. It's like cloud seeding, or water condensing on the side of a g Adding impurities on purpose is called inoculation Growth and Solidification - Grain Size Solidification caused by homogeneous nucleation occurs suddenly, and only produces a few grains In heterogeneous nucleation, solidification occurs on many "seeds", so the grains are smaller, and more uniform If a melt is cooled slowly, and the temperature is the same throughout, solidification occurs with equal probability everywhere in the melt. Metals are usually cooled from the container walls - so solidification starts on the walls Nucleation vs. Crystal Growth (solution or melt) Undercooling - cooling below the melting point relations between undercooling, nucleation rate and growth rate of the nuclei large undercooling: many small nuclei (spontaneous nucleation) growth rate small small undercooling: few (evtl. small) nuclei growth rate high 21 Nucleation vs Rate of nucleation Rate of growth Ta = small undercooling, slow cooling rate Fast growth, slow nucleation = Few coarse crystals Tb = larger undercooling, rapid cooling rate Rapid nucleation, slow growth = many fine-grained crystals Tc = very rapid cooling Nearly no nucleation = glass Crystal Growth Tc t T. £ i 5 Nucleation A aj 'S a: 4 s. t \ l I 1 \ 1 1 1 1 Tůmtiůrůtí irü ^ Itíll ipyi aLUl tí r Heat of Fusion When the liquid solidifies, energy must be removed. In planar growth the energy is conducted into the solid and out through the walls of the container If the melt is not well inoculated Solidification starts on the walls The surrounding liquid is supercooled, so the solid quickly grows All heat that is evolved is hard to conduct away Some of it is absorbed by the surrounding liquid which then heats up 23 Growth of Single Crystals CZOCHRALSKI or KYROPOULOS METHOD Crystal pulling technique Single crystal growth from the melt precursor(s) Crystal seed placed in contact with surface of melt Temperature of melt held just above melting point = highest viscosity, lowest vapor pressure Seed gradually pulled out of the melt, 1 mm per hour Melt solidifies on surface of seed Melt and seed usually rotated counterclockwise with respect to each other to maintain constant temperature and to facilitate uniformity of the melt during crystal growth, 10 rpm Produces higher quality crystals, less defects Inert atmosphere, often under pressure around growing crystal and melt to prevent any materials loss Jan Czochralski (1885-1953) 24 Growth of Single Crystals CZOCHRALSKI or KYROPOULOS METHOD Simett- Heater-Inert gas(Ar) <^ j> 2-50 rpm Si seed Si SiriCjlO crystal crucible Susceptor (graphite) 25 Diam 300 mm Length 2 m Weight 265 kg 26 Growth of Single Crystals Growing bimetallic crystals like GaAs Layer of molten inert oxide like B203 spread on to the molten feed material to prevent preferential volatilization of the more volatile component of the bimetal critical for maintaining precise stoichiometry for example Ga1+xAs and GaAs1+x which are respectively rich in Ga and As, become p-doped and n-doped Growth of Single Crystals The Czochralski crystal pulling technique for growing large single crystals in the form of a rod subsequently cut and polished for various applications Si Ge GaAs LiNb03 SrTi03 NdCa(Nb03)2 28 Six steps in the CZ growth of a silicon single crystal: a) Evacuation and heating of the polycrystalline silicon ("pumping") b) Setting the temperature of the Si melt just above 1414 °C ("melting") c) Dipping the thin Si seed crystal into the homogeneous Si melt ("dipping") d) Initiating crystallization at the neck of the thin Si seed ("necking") e) Adjustment of the shoulder of the desired single crystal diameter ("shoulder"; four positions which portray the fourfold drawing axis [100] are visible at the hot, light marginal zone of the single crystal) f) Growing phase of the single crystal with constant diameter ("body"). 29 Growth of Single Crystals STOCKBARGER AND BRIDGMAN METHODS Stockbarger method is based on a crystal growing from the melt, involves the relative displacement of melt and a temperature gradient furnace, fixed gradient and a moving melt/crystal Temperature gradient Boat Melt ' Crystal Original seed Pulling ~*~ direction 30 Growth of Single Crystals STOCKBARGER AND BRIDGMAN METHODS Bridgman method is again based on crystal growth from a melt, but now a temperature gradient furnace is gradually cooled and crystallization begins at the cooler end, fixed crystal and changing temperature gradient t 0) 0) Q. .0) Boat Temperature gradient Crystal Original seed 31 Both methods are founded on the controlled solidification of a stoichiometric melt of the material to be crystallized Enables oriented solidification Melt passes through a temperature gradient Crystallization occurs at the cooler end Both methods benefit from seed crystals and controlled atmospheres (sealed containers) crystal mp (°C) velocity of grad. container material A1203 2037 2-8 mm h1 Mo FeAl204 1790 5-10 Ir Cu 1083 6-60 graphite AgBr 434 1-5 Pyrex Ar(!) -189 0.5-1.5 Mylar 32 Zone Melting Purification of solids Crystal growth Thermal profile furnace, RF, arc, electron beam heating Material contained in a boat (must be inert to the melt) Only a small region of the charge is melted at any one time Initially part of the melt is in contact with the seed Boat containing sample pulled at a controlled velocity through the thermal profile furnace - zone of material melted Oriented solidification of crystal occurs on the seed t j-------------------J- -\------- Tern peratu re gradient | : £ ! '_______ Pulling ŕ Boaí -*-^2ZB5S3& , mtlfflÉ^------*- direction Crystal or Melt' Crystal ^inal powder 33 Zone Zone refining methods for purifying solids Partitioning of impurities occurs between melt and the crystal Impurities concentrate in liquid more than the solid phase, swept out of crystal by moving the liquid zone Used for purifying materials like W, Si, Ge to ppb level of impurities, often required for device applications Melting Liquid is kC C CK % Impurity —» C) c ItC /S0lj6\; ^ 0 Distance * W#A ■ p h.' --'-í M ooo—* JÍ FumacD tolls OOO kC - rr Ck Zone Melting - a small slice of the sample is molten and moved continuously along the sample - impurities normally dissolve preferably in the melt (!! icebergs in salt water don't contain any salt!!) - segregation coefficient k: K = Csoliď Cliquid (c: concentration of an impurity) only impurities with k < 1 can be removed by zone melting !! 35 Zone Melting Distance, x ©©©-*- @i@©—*- ©©©-*■■ ©©©-*■ ©©©-*- _ , ^™ j ■ ■ ■ ^ ■ ------ p ■ i i i ■ i ^™ fc h * I ' ■ I B ■ 4 T ■ ■ J ■J ---- r ' ■ . h "■,■■■■■ — i......' ,*■'.. . • _"*'*■ " i__ " B L ■ r " ^^ ■ ■ ■ 4 ■ __ » L h I ■ ■ __ ■ ©©©->- ©©©-*- ©©©-*" ©@©-*- ©©©->- A multi-heater arrangement gives much faster zone refining Zone Melting FLOATING ZONE METHOD Molten zone is confined by surface tension between a polycrystalline ingot and a single-crystal seed Holder I Heater m i Molten zone Ingot Pulling direction 37 VERNEUIL FUSION FLAME METHOD 1904 first recorded use of the method Useful for growing crystals of extremely high melting metal oxides Examples include: Ruby from Cr3+/Al203 powder Sapphire from Cr26+/Al203 powder Spinel, CoO, ferrites vibrator n L_ \ oxygen oxygen water :at powder •"^hydrogen IF *- water Starting material fine powder Passed through 02/H2 flame or plasma torch Melting of the powder occurs in the flame Molten droplets fall onto the surface of a seed or growing crystal Controlled crystal growth jjjjl^- single crystal "hr 1 furnace I 38 Ceramic Crystal Figure 5.1 A system for the Vcrneiiil growth oľoxidic materials. Note that the burner is composed ofthree coaxial lubes. Some workers use more tubes, and there are also designs using many small parallel lubes. With these it is possible to produce wider names, and by having independent controls on various sets oftubes it is possible lo optimize the heal input to givea nearly flat growth face on a large crystal. THE FLUX METHOD Material dissolved in a suitable flux = solvent (metals, fluorides, oxides), lower melting point than the pure solute Single crystals grown from supersaturated solution Suitable for materials which: ♦ vaporize or dissociate at temperatures above their mp ♦ there are no suitable containers at elevated temperatures Material Flux As Ga B Pt Si,Ge Pb, Zn, Sn GaAs, GaP Pb, Zn, Sn BaTi03 KF ZnO PbF2 ZnS SnF2 MgFe204 NaF C03O4 B203 - PbO Fe203 Na2B407 Ti02 Na2B407 - B20 THE FLUX METHOD AIF3 2.0 g of AIF3,25.0 g of PbCl2, 2.5 g PbF2 24 h at 1200 K, cooled at 4 deg h1 down to 723 K thick platelets and small cubes 41 THE SOLUTION METHOD Suitable for materials with a reasonable solubility in the selected solvent: water, organic solvents, NH3(1), HF, S02(1) Nucleation homogeneous heterogeneous Dilute solution, solvent with low solubility for given solute Supersaturated solution, seed crystals Single crystals grown at constant supersaturation Techniques: ♦ slow evaporation ♦ slow cooling ♦ vapor diffusion ♦ solvent diffusion ♦ reactant diffusion ♦ recirculation, thermal differential, convection ♦ cocrystallants (OPPh3 for organic proton donors) ♦ counterion, similar size of cation and anion least soluble ♦ ionization of neutral compounds, protonation/deprotonation, hydrogen bonding Rochelle salt: öf-NaKC4H406.4H20 (tartrate) KDP alum KDP crystals (KH2P04) grown from supersaturated solution crystal seed slow cooling a frequency converter -converts the infrared light at 1053 nm into the ultraviolet at 351 nm 43 HYDROTHERMAL SYNTHESIS Water medium High temperature growth, above normal boiling point Water acts as a pressure transmitting agent Water functions as solublizing phase Often a mineralizing agent is added to assist with the transport of reactants and crystal growth Speeds up chemical reactions between solids Crystal growth hydrothermally involves: Temperature gradient reactor = autoclave (bomb !!) Dissolution of reactants at one end Transport with help of mineralizer to seed at the other end Crystallization at the other end HYDROTHERMAL SYNTHESIS Useful technique for the synthesis and crystal growth of phases that are unstable in a high temperature preparation in the absence of water materials with low solubility in water below 100 °C Some materials have negative solubility coefficients, crystals can grow at the hotter end in a temperature gradient hyrdothermal reactor Example: 0t-AlPO4 (Berlinite) important for its high piezoelectric coefficient (larger than a-quartz with which it is isoelectronic) used as a high frequency oscillator Hydrothermal growth of quartz crystals Water medium, nutrients 400 °C, seed 360 °C, pressure 1.7 kbar Mineralizer IM NaOH Uses of single crystal quartz: Radar, sonar, piezoelectric transducers, monochromators, XRD Annual global production hundreds of tons of quartz crystals 45 HYDROTHERMAL SYNTHESIS Hydrothermal crystal growth is also suitable for growing single crystals of: Ruby: Cr3+/Al203 Corundum: a-Al203 Sapphire: Cr26+/Al203 Emerald: Cr3+/Be3Al2Si6018 Berlinite: a-AlP04 Metals: Au, Ag, Pt, Co, Ni, Tl, As Role of the mineralizer: Control of crystal growth rate: choice of mineralizer, temperature and pressure Solubility of quartz in water is important 46 HYDROTHERMAL SYNTHESIS Si02 + 2H20 <-> Si(OH)4 0.3 wt% even at supercritical temperatures >374 °C A mineralizer is a complexing agent (not too stable) for the reactants/precursors that need to be solublized (not too much) and transported to the growing crystal Some mineralizing reactions: NaOH mineralizer, dissolving reaction, 1.3-2.0 kbar 3Si02 + 60H <-> SÍ3O96 + 3H20 Na2C03 mineralizer, dissolving reaction, 0.7-1.3 kbar Si02 + 20H <-> Si032 + H20 CO32 + H20 <-> HCO3 + OH NaOH creates growth rates about 2x greater than with Na2C03 because of different concentrations of hydroxide mineralizer HYDROTHERMAL SYNTHESIS Examples of hydrothermal crystal growth and mineralizers Berlinite a-AlP04 Powdered A1P04 cool end of reactor negative solubility coefficient!!! H3PO4/H2O mineralizer, AIPO4 seed crystal at hot end Emeralds Cr3+/Be3Al2Si6018 Si02 powder at hot end 600 °C, NH4CI or HC1/H20 mineralizer, 0.7-1.4 kbar, cool central region for seed, 500 °C, Al203/BeO/Cr3+ dopant powder mixture at other hot end 600 °C 6Si02 + AI2O3 + 3BeO -> Be3Al2Si6018 Beryl contains Si601812" six rings HYDROTHERMAL SYNTHESIS Metal crystals Metal powder at cool end 480 °C, Mineralizer 10M HI/I2 Metal seed at hot end 500 °C. Dissolving reaction that also transports Au to the seed crystal: Au + 3/2I2 + I" <-» Aul4 Metal crystals grown this way include Au, Ag, Pt, Co, Ni, Tl, As at 480-500 °C Diamonds \t- 1 r 1 u n 800 °c'140 MPa a- a Ni + C + H20----------------► diamond HYDROTHERMAL SYNTHESIS Carbon films on SiC fibers 100 MPa SiC + 2 H20 300'600°c ► C + 2 H2 + Si02 Zeolites Al(OH)3, Si02, NaOH, template Mx/n [(A102)x(Si02U. mH20 HYDROTHERMAL SYNTHESIS necessitates knowledge of what is going on in an autoclave under different degrees of filling and temperature Pressure, volume, temperature tables of dense fluids like water Critical point of water: 374.2 °C, 218.3 bar Density of liquid water decreases with T Density of water vapor increases with T Density of gas and liquid water the same 0.32 gem"3, at the critical point Liquid level in autoclave rises for > 32% volume filling Autoclave filled at 250 °C for > 32% volume filling For 32% volume filling liquid level remains unchanged and becomes fluid at critical temperature 51 HYDROTHERMAL SYNTHESIS 52 HYDROTHERMAL SYNTHESIS Tables of pressure versus temperature for different initial volume filling of autoclave must be consulted to establish a particular set of reaction conditions for a hydrothermal synthesis or crystallization Safety: if this is not done correctly, with proper protection equipment in place, you can have an autoclave explosion that can kill!!! 53 BULK-MATERIAL DISSOLUTION TECHNIQUE large zeolite crystals: up to 3 mm, SOD, MFI, ANA,CAN, JBW autoclave, PTFE liner quartz tube (Si02) TPAOH, HF, H20 200 °C, 25-50 days ceramic tube (Si02, A1203) NaOH, H20 100-200 °C, 7-20 days Small surface area, low dissolution rate, saturation concentration maintained, only a few nuclei are produced at the beginning, no large crystals formed in the stirred reactions, concentration gradients DECOMPLEXATION CRYSTALLIZATION crystallization under ambient conditions, low temperature and pressure, provides kinetic products, control of crystal size and morphology, habit AgX, X = CI, Br, I MX, M = H, Na, K, NH4 Agl + HI 4 * H+ + [Agl2]" aqueous solution overlayer absolute ethanol, HI diffusion, decomplexation of Agl, hexagonal plates 5 mm AgX + 2 NH3 «=► [Ag(NH3)2]+ + X X = CI, Br, slow evaporation (3-5 days), AgX crystals 55 Agl + KI «------► K+ + [Agl2] © concentration gives K[AgI2] crystals © dilution by slow diffusion gives 20 mm Agl crystals © warming gives Agl crystals (inverse temperature dependence of Agl solubility in KI) CuCl + HCl 4 ► H+ + [CuCl2] 4 ► CuCl Hgl2 + KI^=^ [Hgl3] ^=^ [Hgl4]2 ^=^HgI2 PbO + hot KOH solution, slow cooling provides PbO as 2 mm yellow needles and 1 mm red blocks COMPLEXATION-MEDIATED CRYSTALLIZATION Salts with high lattice energy fluorides, carbonates, acetates Solubilized in organic solvents by crown ethers Crystallization provides uncomplexed salts NaOOCCH3.3H20 dissolves in cyclohexane with 15-crown-5 prismatic crystals 57 COMPLEXATION-MEDIATED REACTION CRYSTALLIZATION Two soluble salts react to produce an insoluble phase © aqueous solutions © nonaqueous solvents CaC03 calcite TD stable phase at room temp., in H20 vaterite kinetic product aragonite TD stable at high temperature CaCl2 (in MeOH) + NaHC03 (in MeOH, 18-crown-6) microcrystalline calcite upon aging converts to nanocrystalline vaterite, surface stabilization by surface chelatation THE GEL METHOD Large single crystals ♦ hydrogels: silicagel (water glass), polyvinyl alcohol, gelatin, agar Silicate gel Impregnation with metal or ligand, setting the gel = condensation, crosslinking, pH control of the condensation rate Layered with the solution of ligand or metal Slow diffusion, xtal growth CuS04+ [NH3OH]Cl —► Cu Pb(OAc)2 + Zn —► Pb + Zn(OAc)2 Pb(OAc)2 + KI ___► Pbl2 + 2 KOAc Liesegang rings, agates RbSnBr3, CsSb2I5 semiconductors 59 THE GEL METHOD ♦ nonaqueous gels PEO (MW = 100 000) in 1,2-dichloroethane + MeOH, EtOH, PrOH, DMF, CH3CN, DMSO Impregnation with metal or ligand Layered with the solution of ligand or metal Slow diffusion, crystal growth U-tube, counter-diffusion Concentration programming, increasing concentrations Ostwald rippening = larger xtals grow, smaller dissolve ELECTROCHEMICAL REDUCTIVE SYNTHESIS, CRYSTAL GROWTH Molten mixtures of precursors, product crystallizes from melt Melt electrochemistry: Electrochemical reduction CaTi(IV)03 (perovskite)/CaCl2 (850 °C) -► CaTi(III)204 (spinel) Na2Mo(VI)04/Mo(VI)03 (675 °C) -► Mo(IV)02 (large crystals) Li2B407/LiF/Ta(V)205 (950 °C) -► Ta(II)B2 Na2B407/NaFA^(V)205/Fe(III)203 (850 °C) -► Fe(II)V(III)204 (spinel) Na2Cr04/Na2SiF6 (T °C) -> Cr3Si Na2Ge205/NaF/NiO -> Ni2Ge 61 ELECTROCHEMICAL REDUCTIVE SYNTHESIS, CRYSTAL GROWTH Phosphates -» phosphides Carbonates -» carbides Borates -^ borides Sulfates -» sulfides Silicates -» suicides Germanates -» germides 62 Synthesis of amorphous materials Quenching of molten mixture of metal oxide with a glass former (P205, V205, Bi203, Si02, CaO,...), large cooling rates required (>107 K s1) Ion beam sputtering Thermal evaporation Thermal decomposition of organometallic precursors (Fe(CO)5,...) Cr203, Mn02, Pb02, V205, Fe203 Sonochemical decomposition of organometallic precursors (Fe(CO)5, M(acac)n,... Precipitation on metal hydroxides, transformation to hydrous oxides MW heating of metal salt solution Cr203, Fe203